Specular Channel
HF mobile or ionospheric radiocommunications are affected by the multiple path phenomenon. In urban areas, the transmitted signal is reflected and diffracted on fixed or moving obstacles present in the environment. For HF transmissions, the reflections are made on different layers of the ionosphere. In the case of propagation channels that can be qualified as specular, in other words the transmission takes place along a limited number of discrete or temporary paths characterized by a delay and a complex attenuation. Assuming an observation time compatible with the stationarity duration of the channel, multi-sensor reception and specular propagation, the expression for the multi-sensor channel is:
                              c          ⁡                      (            t            )                          =                              ∑                          k              =              1                        d                    ⁢                                          ⁢                                    a              k                        ⁢                          δ              ⁡                              (                                  t                  -                                      τ                    k                                                  )                                                                        (        1        )            where k is the index of a path, ak is the vector for which the components are complex attenuations of the path k for the different channels, τk is the delay associated with the kth path and d is the number of paths in a channel.
Furthermore, if each path k is incident on the network following a reduced spatial diffusion cone, the expression (1) is in the following form
                              c          ⁡                      (            t            )                          =                              ∑                          k              =              1                        d                    ⁢                                          ⁢                                    β              k                        ⁢                          a              ⁡                              (                                  θ                  k                                )                                      ⁢                          δ              ⁡                              (                                  t                  -                                      τ                    k                                                  )                                                                        (        2        )            where a(θk) is the input vector for an angle associated with the kth path and βk is the complex attenuation of the path.
In the first case (Eq. 1), the channel is not defined by parameters related to the direction from which the paths arrive, each propagation path is defined by parameters consisting of an arrival time τ and an <<antenna vector>> a. Thus, the calibration is no longer necessary and algorithms are no longer limited by spatial dispersion or coherent paths.
In the second case (Eq. 2), paths are defined by parameters consisting of their directions of arrival, which assumes that the type of the antenna is known and therefore generally involves setting up a calibration to estimate the values of θk.
Blind Identification
In active or driven systems, the channel parameters are calculated during a learning phase in which the transmitter transmits a sequence known to the receiver.
If the propagation channel fluctuates in time, particularly due to movements of mobile stations or ionospheric layers, the sequence must be sent periodically in order to update the value of the parameters.
If this type of system is efficient, the regular transmission of a learning sequence can cause a significant reduction in the effective throughput.
For example, in the STANAG 4285 standard for cooperative ionospheric HF transmissions, half of the transmitted symbols are learning symbols.
Prior art also includes different blind methods and systems, in which parameters are estimated starting from statistics of the received signal, without any advance knowledge of the learning sequence.
Second Order Techniques
For example, the proposed techniques simply use second order statistics (space-time covariance matrix) of the received signal. Second order algorithms have better convergence properties than higher order algorithms, i.e. the variance of second order estimators for a given number of symbols, is usually less than the variance of estimators with higher orders. Furthermore, they have fewer local optimisation problems than techniques with higher orders.
Various methods and algorithms have been developed, such as those described in document entitled “Multichannel Blind Identification : from subspace to maximum likelihood methods” by L. Tong and S. Perreau; Proceedings of the IEEE, 86(10): 1951-1967, October 1998. One of the disadvantages of these algorithms is that the length of the global transmission channel has to be known, and most of them are intolerant to an error in the estimate of this length. When the bandwidth of the transmission is limited, the channel length is only defined approximately and these algorithms can no longer be used.
State of the Art for Blind Parametric Identification
Most work on blind identification of characteristic propagation parameters uses decoupled algorithms, i.e. algorithms that independently estimate arrival times and antenna vectors or arrival directions. These include direction finding algorithms to estimate directions of arrival, and coherent source separation algorithms to estimate antenna vectors. A lot of work has also be done on estimating arrival times.
Joint estimating methods can improve the precision and resolution of estimators, such that parameters can be estimated even when delays (or angles) are very similar.
The main work done on blind joint estimating of parameters (θ,τ) is described in the following references:                “Identification spatio-temporelle de canaux de propagation à trajets multiples” (“Space-time identification of multipath propagation channels) by J. Gouffraud, PhD thesis, Ecole Normale Supérieure de Cachan, 1997, and        “Improved blind channel identification using a parametric approach” by M. C. Vanderveen and A. Paulraj, IEEE Communications Letters, pages 226-228, August 1998.        
The idea is that criteria used to make a blind estimate of the pulse response may be directly minimized as a function of the angles and delays, using subspace type criteria like those described in the “Subspace methods for the blind identification of multichannel FIR filters” paper by E. Moulines, P. Duhamel, J-F. Cardoso and S. Mayrargue, IEEE Trans. on signal Processing, 43(2): 516-525, February 1995. These algorithms require that the transmission/reception filter is known in advance and that the antenna is calibrated.
Furthermore, an example of a method of making a joint blind estimate of parameters (a,τ) is described in the “Methods for blind equalization and resolution of overlapping echoes of unknown shape” paper by A. Swindlehurst and J. Gunther, IEEE Trans. on Signal Processing, 47(5): 1245-1254, May 1999. The authors work in the frequency range and propose an iterative IQML type algorithm to give an approximate solution with a maximum probability and an explicit initialisation algorithm based on the ESPRIT algorithm. These algorithms do not require advance knowledge of the transmission filter, but do have the disadvantage that a Fourier transformation is necessary before processing.